I was expecting them to put forward an existential risk (rogue AI), but this seems much more mundane. Granted, they might be downplaying that angle to taken more seriously. However, from a mundane perspective, the main issue that you have with arms races is not both sides having a technology, but one side having the tech, and willing to go to war to prevent the other side from getting it (see for example, Cuba, Iraq, Iran).
Furthermore, as they point out, you don't need access to special materials, or laboratories. The main reason that nukes are controllable is not primarily due to the science being secret (it's mostly not at this point), or hard to rederive (it's really not), but that you have to build up a ton of ore refinement plants to get enough U235 (other fissile material) to actually build the bomb. And it's really hard to do that in secret (or cheaply). Nothing makes the Manhatten project any cheaper today, and it cost about 23 billion dollars in today's dollars, and it involved 130,000 (twice the size of Google) people.
However, with Autonomous weapons, you don't need anywhere nearly as many people (Google X has on the order of 250 people[1]), or resources, and it can (as the article itself points out) be done much cheaper. In a few years, all the necessary components could even be conceivably cobbled together from Github projects. Any nation could easily fund it, likely without being detected, or even it being clear that they were aware that the "R&D" dollars were being used in such a way.
Given that, banning it seems like it would actually lead to more warfare, as the US would take it on itself to enforce the ban, and declare 'pre-emptive' strikes on nations that had a secret Autonomous Research project.
